MIMIC III Exploratory Data Analysis

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from feature_engine.imputation import RandomSampleImputer

mimic_time_data = pd.read_csv("mimicfull.csv")
mimic_time_data.head()

	SUBJECT_ID	CHARTTIME	MEASUREMENT	VALUENUM	LOS	GENDER	ETHNICITY	AGE	DIED_DURING_ICU_STAY	OUTTIME
0	18992	2124-05-15 18:51:00.000 Z	Potassium	3.900000	104.2483	M	WHITE	40.0	0	2124-08-03 12:09:45.000 Z
1	18992	2124-05-15 18:51:00.000 Z	Glucose	116.000000	104.2483	M	WHITE	40.0	0	2124-08-03 12:09:45.000 Z
2	18992	2124-05-15 19:00:00.000 Z	Diastolic blood pressure	52.000000	104.2483	M	WHITE	40.0	0	2124-08-03 12:09:45.000 Z
3	18992	2124-05-15 19:00:00.000 Z	Temperature	36.722221	104.2483	M	WHITE	40.0	0	2124-08-03 12:09:45.000 Z
4	18992	2124-05-15 19:00:00.000 Z	Peripheral oxygen saturation	92.000000	104.2483	M	WHITE	40.0	0	2124-08-03 12:09:45.000 Z

mimic_time_data.shape

(27635100, 10)

The time series data extracted from the MIMIC database contains over 2.7 million observations and 10 columns. Each patient is identified by SUBJECT_ID, and CHARTTIME records when medical tests were conducted. The MEASUREMENT and VALUENUM columns capture vital signs and laboratory results. LOS represents the length of ICU stay in fractional days, while GENDER, ETHNICITY, and AGE provide demographic information. The DIED_DURING_ICU_STAY column indicates patient survival status in the ICU, and OUTTIME notes the discharge time or time of death.

mimic_time_data.columns = mimic_time_data.columns.str.lower()
mimic_time_data['charttime'] = pd.to_datetime(mimic_time_data['charttime'])
mimic_time_data['outtime'] = pd.to_datetime(mimic_time_data['outtime'])

Next, we filter for vital signs and laboratory test results recorded during the last 24 hours before patient discharge. If multiple records exist for a patient, we calculate the average. The results are then recorded into new columns.

# Filter rows within 24 hours before discharge
mimic_24hrs = mimic_time_data[(mimic_time_data['charttime'] >= mimic_time_data['outtime'] - pd.Timedelta(hours=24)) & (mimic_time_data['charttime'] <= mimic_time_data['outtime'])]

# Group by subject_id and measurement, and calculate the mean of valuenum
mimic_aggregated = mimic_24hrs.groupby(['subject_id', 'measurement']).valuenum.mean().reset_index()

# Pivot the table to create new columns for each measurement
mimic_pivoted = mimic_aggregated.pivot(index='subject_id', columns='measurement', values='valuenum').reset_index()

# Merge with the additional columns from the same subject_id
mimic_final = mimic_24hrs[['subject_id', 'age', 'gender', 'ethnicity', 'los', 'died_during_icu_stay']].drop_duplicates(subset='subject_id')
mimic = mimic_pivoted.merge(mimic_final, on='subject_id', how='left')

# Rename columns with custom names
custom_columns = {
    'Diastolic blood pressure': 'dbp',
    'Systolic blood pressure': 'sbp',
    'Mean arterial pressure': 'map',
    'Temperature': 'temp',
    'Peripheral oxygen saturation': 'spo2',
    'Heart rate': 'heart_rate',
    'Respiratory rate': 'resp_rate',
    'Albumin': 'albumin',
    'Blood urea nitrogen': 'bun',
    'Bilirubin': 'bilirubin',
    'Lactate': 'lactate',
    'Bicarbonate': 'bicarbonate',
    'Band neutrophil': 'neutrophils',
    'Chloride': 'chloride',
    'Creatinine': 'creatinine',
    'Glucose': 'glucose',
    'Hematocrit': 'hematocrit',
    'Hemoglobin': 'hemoglobin',
    'Platelet count': 'platelets',
    'Potassium': 'potassium',
    'Partial thromboplastin time': 'ptt',
    'Sodium': 'sodium',
    'White blood cells': 'wbc', 
    'died_during_icu_stay': 'death_status'
}

mimic.rename(columns=custom_columns, inplace=True)

# Display the resulting DataFrame
display(mimic.head())

	subject_id	albumin	neutrophils	bicarbonate	bilirubin	bun	chloride	creatinine	dbp	glucose	...	resp_rate	sodium	sbp	temp	wbc	age	gender	ethnicity	los	death_status
0	3	NaN	NaN	23.0	NaN	17.0	96.0	1.3	55.545455	85.0	...	20.363636	131.500000	116.863636	35.930556	10.5	76.0	M	WHITE	6.0646	0
1	6	NaN	NaN	14.0	0.3	73.0	101.0	5.1	64.047619	118.0	...	14.347826	130.000000	153.523810	36.039682	3.9	66.0	F	WHITE	3.6729	0
2	9	NaN	NaN	24.0	NaN	33.0	107.0	2.0	76.476190	114.0	...	16.653846	135.666667	141.666667	35.888889	11.1	41.0	M	UNKNOWN/NOT SPECIFIED	5.3231	1
3	12	2.5	NaN	23.0	7.7	29.0	100.0	1.1	75.450000	130.0	...	31.400000	135.000000	146.300000	37.074074	30.2	72.0	M	WHITE	7.6348	1
4	13	NaN	NaN	29.0	NaN	13.0	104.0	0.4	60.520000	168.5	...	18.840000	138.000000	125.440000	37.687301	14.3	40.0	F	WHITE	3.6660	0

5 rows × 29 columns

mimic.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 18830 entries, 0 to 18829
Data columns (total 29 columns):
 #   Column        Non-Null Count  Dtype  
---  ------        --------------  -----  
 0   subject_id    18830 non-null  int64  
 1   albumin       1986 non-null   float64
 2   neutrophils   710 non-null    float64
 3   bicarbonate   17441 non-null  float64
 4   bilirubin     3113 non-null   float64
 5   bun           17516 non-null  float64
 6   chloride      17491 non-null  float64
 7   creatinine    17519 non-null  float64
 8   dbp           18748 non-null  float64
 9   glucose       17516 non-null  float64
 10  heart_rate    18789 non-null  float64
 11  hematocrit    17492 non-null  float64
 12  hemoglobin    17289 non-null  float64
 13  lactate       1529 non-null   float64
 14  map           18738 non-null  float64
 15  ptt           9430 non-null   float64
 16  spo2          18693 non-null  float64
 17  platelets     17302 non-null  float64
 18  potassium     17667 non-null  float64
 19  resp_rate     18737 non-null  float64
 20  sodium        17528 non-null  float64
 21  sbp           18750 non-null  float64
 22  temp          18653 non-null  float64
 23  wbc           17300 non-null  float64
 24  age           18830 non-null  float64
 25  gender        18830 non-null  object 
 26  ethnicity     18830 non-null  object 
 27  los           18830 non-null  float64
 28  death_status  18830 non-null  int64  
dtypes: float64(25), int64(2), object(2)
memory usage: 4.2+ MB

round(mimic.isna().mean()*100, 2)

subject_id       0.00
albumin         89.45
neutrophils     96.23
bicarbonate      7.38
bilirubin       83.47
bun              6.98
chloride         7.11
creatinine       6.96
dbp              0.44
glucose          6.98
heart_rate       0.22
hematocrit       7.11
hemoglobin       8.18
lactate         91.88
map              0.49
ptt             49.92
spo2             0.73
platelets        8.11
potassium        6.18
resp_rate        0.49
sodium           6.91
sbp              0.42
temp             0.94
wbc              8.13
age              0.00
gender           0.00
ethnicity        0.00
los              0.00
death_status     0.00
dtype: float64

The resulting dataset contains information on the last 24 hours in the ICU for individual patients, identified by unique subject_id. It includes 18,830 patients and 29 columns. All columns, except for demographics and death_status, have missing values. Neutrophils has the most missing values at 96%, followed by Lactate at 92%, Albumin at 89%, Bilirubin at 83%, and PTT at 50%.

mimic.head()

	subject_id	albumin	neutrophils	bicarbonate	bilirubin	bun	chloride	creatinine	dbp	glucose	...	resp_rate	sodium	sbp	temp	wbc	age	gender	ethnicity	los	death_status
0	3	NaN	NaN	23.0	NaN	17.0	96.0	1.3	55.545455	85.0	...	20.363636	131.500000	116.863636	35.930556	10.5	76.0	M	WHITE	6.0646	0
1	6	NaN	NaN	14.0	0.3	73.0	101.0	5.1	64.047619	118.0	...	14.347826	130.000000	153.523810	36.039682	3.9	66.0	F	WHITE	3.6729	0
2	9	NaN	NaN	24.0	NaN	33.0	107.0	2.0	76.476190	114.0	...	16.653846	135.666667	141.666667	35.888889	11.1	41.0	M	UNKNOWN/NOT SPECIFIED	5.3231	1
3	12	2.5	NaN	23.0	7.7	29.0	100.0	1.1	75.450000	130.0	...	31.400000	135.000000	146.300000	37.074074	30.2	72.0	M	WHITE	7.6348	1
4	13	NaN	NaN	29.0	NaN	13.0	104.0	0.4	60.520000	168.5	...	18.840000	138.000000	125.440000	37.687301	14.3	40.0	F	WHITE	3.6660	0

5 rows × 29 columns

mimic = mimic.drop(columns=['subject_id'])

Demographic features

There are three features related to demographic information: gender, ethnicity, and age. We examine the distribution of these features.

Gender

mimic["gender"].value_counts(normalize=True)

gender
M    0.559426
F    0.440574
Name: proportion, dtype: float64

The dataset is composed of 56% male patients and 44% female patients.

sns.set(style="dark", palette="icefire")
sns.countplot(mimic, x="gender", hue='death_status')

<Axes: xlabel='gender', ylabel='count'>

The side-by-side bar plot shows that the pattern of death status is similar for both genders, thus there is no association between the two variables.

Ethnicity

mimic.ethnicity.value_counts()

ethnicity
WHITE                                         13196
UNKNOWN/NOT SPECIFIED                          2021
BLACK/AFRICAN AMERICAN                         1306
HISPANIC OR LATINO                              450
OTHER                                           428
UNABLE TO OBTAIN                                399
ASIAN                                           282
PATIENT DECLINED TO ANSWER                      188
ASIAN - CHINESE                                  89
HISPANIC/LATINO - PUERTO RICAN                   68
BLACK/CAPE VERDEAN                               52
WHITE - RUSSIAN                                  48
MULTI RACE ETHNICITY                             37
WHITE - OTHER EUROPEAN                           28
HISPANIC/LATINO - DOMINICAN                      27
BLACK/HAITIAN                                    23
ASIAN - ASIAN INDIAN                             20
WHITE - BRAZILIAN                                20
PORTUGUESE                                       18
ASIAN - VIETNAMESE                               17
MIDDLE EASTERN                                   15
BLACK/AFRICAN                                    15
AMERICAN INDIAN/ALASKA NATIVE                     9
HISPANIC/LATINO - GUATEMALAN                      9
ASIAN - CAMBODIAN                                 8
WHITE - EASTERN EUROPEAN                          8
ASIAN - OTHER                                     8
ASIAN - FILIPINO                                  7
NATIVE HAWAIIAN OR OTHER PACIFIC ISLANDER         7
HISPANIC/LATINO - CUBAN                           4
HISPANIC/LATINO - SALVADORAN                      4
HISPANIC/LATINO - COLOMBIAN                       3
HISPANIC/LATINO - MEXICAN                         3
ASIAN - KOREAN                                    3
HISPANIC/LATINO - CENTRAL AMERICAN (OTHER)        3
ASIAN - THAI                                      2
ASIAN - JAPANESE                                  2
HISPANIC/LATINO - HONDURAN                        1
SOUTH AMERICAN                                    1
CARIBBEAN ISLAND                                  1
Name: count, dtype: int64

Ethnicity comprises various groups. We will combine some due to overlaps and categorize the remaining groups as "Other".

def categorize_ethnicity(ethnicity):
    """Categorize ethnicity into 5 groups: White, Black, Hispanic/Latino, Asian, and Other"""
    ethnicity = ethnicity.lower()
    if 'white' in ethnicity:
        return 'White'
    elif 'black' in ethnicity or 'AFRICAN' in ethnicity:
        return 'Black'
    elif 'hispanic' in ethnicity or 'latino' in ethnicity:
        return 'Hispanic/Latino'
    elif 'asian' in ethnicity:
        return 'Asian'
    else:
        return 'Other'

mimic['ethnicity'] = mimic['ethnicity'].apply(categorize_ethnicity)
mimic['ethnicity'].value_counts(normalize=True)

ethnicity
White              0.706320
Other              0.165905
Black              0.074137
Hispanic/Latino    0.030377
Asian              0.023261
Name: proportion, dtype: float64

After combining similar ethnicities, the patient distribution is 71% White, 17% Other, 7% Black, 3% Hispanic/Latino, and 2% Asian.

sns.set(style='dark', palette='icefire')
sns.countplot(mimic, x='ethnicity', hue='death_status')

<Axes: xlabel='ethnicity', ylabel='count'>

Similar to patients' gender, the pattern of death status is consistent across all ethnicities, indicating no significant association between them.

We then examine at the distribtuuion of patients' age.

Age

fig, axs = plt.subplots(1, 2, figsize=(10, 5))

# Histogram
axs[0].hist(mimic['age'], bins=25, color='skyblue', edgecolor='black')
axs[0].set_title('histogram of age')
axs[0].set_xlabel('age')
axs[0].set_ylabel('Frequency')

# Box plot
axs[1].boxplot(mimic['age'], vert=False)
axs[1].set_title("distribution of patient's age")
axs[1].set_xlabel("age")

plt.tight_layout()
plt.show()

print(f"minimum age: {min(mimic['age'])}, maximum age: {max(mimic['age'])}")

minimum age: 15.0, maximum age: 91.4

The patients range in age from a minimum of 15 to a maximum of 91, with the majority being over 50 years old. The age distribution is left-skewed, with some outliers present at the lower end.

Medical information

Next, we explore the distribution of medical features, which include vital signs and laboratory tests. First, we examine the typical length of ICU stays for patients.

fig, axs = plt.subplots(1, 2, figsize=(10, 5))

# Histogram
axs[0].hist(mimic['los'], bins=25, color='skyblue', edgecolor='black')
axs[0].set_title(f'typical length of stay in icu')
axs[0].set_xlabel('days')
axs[0].set_ylabel('frequency')

# Box plot
axs[1].boxplot(mimic['los'], vert=False)
axs[1].set_title(f'distribution of length of stay')
axs[1].set_xlabel("days")

plt.tight_layout()
plt.show()

print(f"minimum stay: {min(mimic['los'])}, maximum stay: {max(mimic['los'])}")

minimum stay: 2.0, maximum stay: 153.928

The distribution of ICU stay durations is right-skewed, with many outliers at the upper end. The minimum duration is 2 days, while the maximum is 154 days. Most patients stayed in the ICU for less than 10 days.

We next look at how the LOS differs between patients who died during their ICU stay and those who survived.

plt.figure(figsize=(10, 6))
    
for cls in mimic['death_status'].unique():
    subset = mimic[mimic['death_status'] == cls]
    plt.hist(subset['los'], alpha=0.5, bins=50, label=f'Class {cls}')

plt.title('Histogram of LOS')
plt.xlabel('LOS in Days')
plt.ylabel('Frequency')
plt.legend()
plt.show()

The histogram highlights that most patients, regardless of their outcome, tend to have shorter ICU stays, with a small number of patients experiencing longer stays.

Next, we take a closer look at the vital signs and laboratory test features.

Vital signs

There are seven vital signs present:

• Temperature (°C)
• Diastolic blood pressure (mmHg)
• Systolic blood pressure (mmHg)
• Mean arterial blood pressure (mmHg)
• Peripheral oxygen saturation (%)
• Heart rate (bpm)
• Respiratory rate (breaths/min)

Before we begin, we first examine at the ranges of the columns.

vital_signs = ['heart_rate', 'dbp', 'sbp', 'map', 'temp', 'spo2', 'resp_rate']

min_max_values = mimic[vital_signs].select_dtypes(include=['number']).agg(['min', 'max'])
min_max_values

	heart_rate	dbp	sbp	map	temp	spo2	resp_rate
min	36.6875	20.307692	0.00	26.833333	2.507937	8.666667	5.888889
max	159.0000	5117.761905	4747.68	3138.363030	143.263889	133403.960000	161.086957

Based on literature, the valid ranges for the vital signs are as follows:

• Diastolic BP (dbp): 0 to 375 mmHg
• Systolic BP (sbp): 0 to 375 mmHg
• Mean arterial pressure (map): 14 to 330 mmHg
• Temperature (temp): 26 to 45 °C
• Peripheral oxygen saturation (spo2): 0 to 100%
• Heart rate (heart_rate): 0 to 350 bpm
• Respiratory rate (resp_rate): 0 to 300 breaths/min

If our vital signs fall outside these ranges, they will be replaced with NaN.

Examining the ranges of vital signs shows that DBP, SBP, MAP, Temp, and SpO2 exceed the valid ranges, so we replace these values with NaN.

valid_ranges = {'dbp': (0, 375), 'sbp': (0, 375), 'map': (14, 330), 'temp': (26, 45),
                'spo2': (0, 100), 'heart_rate': (0, 350), 'resp_rate': (0, 300)
}

for column, (lower, upper) in valid_ranges.items():
    mimic[column] = mimic[column].apply(lambda x: x if lower <= x <= upper else np.nan)

mimic[vital_signs].select_dtypes(include=['number']).agg(['min', 'max'])

	heart_rate	dbp	sbp	map	temp	spo2	resp_rate
min	36.6875	20.307692	0.000000	26.833333	26.288889	8.666667	5.888889
max	159.0000	309.720000	196.181818	322.000000	44.918056	100.000000	161.086957

We then examine the distribution of these vital signs.

def plot_histogram_and_boxplot(df, column):
    """
    Plot histogram and box plot for a specified column in a DataFrame.

    Parameters:
    df (pd.DataFrame): DataFrame containing the data.
    column (str): Column name to plot.
    xlabel_hist (str): Label for the x-axis of the histogram.
    xlabel_box (str): Label for the x-axis of the box plot.
    title_hist (str): Title for the histogram.
    title_box (str): Title for the box plot.

    Returns:
    None
    """
    fig, axs = plt.subplots(1, 2, figsize=(10, 5))

    # Histogram
    axs[0].hist(df[column].dropna(), bins=25, color='skyblue', edgecolor='black')
    axs[0].set_title(f"distribution of {column}")
    axs[0].set_ylabel('Frequency')

    # Box plot
    df.boxplot(column=column, vert=False, grid=False)
    axs[1].set_title(f"boxplot of {column}")

    plt.tight_layout()
    plt.show()

    # print(f'Minimum value of {column}: {df[column].min()}')
    # print(f'Maximum value of {column}: {df[column].max()}')
    # print(f'Number of missing values in {column}: {df[column].isna().sum()}')

# loop through each vital sign and call the function
for column in vital_signs:
    plot_histogram_and_boxplot(
        df=mimic,
        column=column
    )

Heart rate and SBP appear to have fairly uniform distributions, with outliers present at both the lower and higher ends. The distributions of DBP, MAP, temperature, and respiratory rate are right-skewed, with extreme values on both ends. Temperature is clustered around 37°C, with the majority of values falling within the expected body temperature range. SpO2 is left-skewed, with saturation in the majority of patients and extreme values at the lower end.

Laboratory measures

There are 16 laboratory measures present:

• Albumin (g/dL)
• Blood urea nitrogen (mg/dL)
• Bilirubin (mg/dL)
• Lactate (mmol/L)
• Bicarbonate (mEq/L)
• Band neutrophils (%)
• Chloride (mEq/L)
• Creatinine (mg/dL)
• Glucose (mg/dL)
• Hemoglobin (g/dL)
• Hematocrit (g/dL)
• Platelet count (1000/mm^3)
• Potassium (mEq/L)
• Partial thromboplastin time (s)
• Sodium (mEq/L)
• White blood cells (1000/mm^3)

Let's examine the ranges of these laboratory measures.

lab_measures = ["albumin", "bun", "bilirubin", "lactate", "bicarbonate", "neutrophils",
    "chloride", "creatinine", "glucose", "hematocrit", "hemoglobin",
    "platelets", "potassium", "ptt", "sodium", "wbc"]

mimic[lab_measures].select_dtypes(include=['number']).agg(['min', 'max']).T

	min	max
albumin	1.000000	5.800000
bun	1.000000	241.000000
bilirubin	0.000000	62.100000
lactate	0.300000	28.100000
bicarbonate	5.000000	51.000000
neutrophils	0.000000	57.000000
chloride	74.250000	140.000000
creatinine	0.000000	15.300000
glucose	8.000000	710.000000
hematocrit	8.700000	55.500000
hemoglobin	2.300000	18.000000
platelets	5.000000	1783.000000
potassium	2.400000	8.500000
ptt	17.500000	150.000000
sodium	101.666667	179.333333
wbc	0.100000	351.100000

The valid ranges for the lab measures are as follows:

• Albumin: 0.6 to 6 g/dL
• Blood urea nitrogen (BUN): 0 to 250 mg/dL
• Bilirubin: 0.1 to 60 mg/dL
• Lactate: 0.4 to 30 mmol/L
• Bicarbonate: 0 to 60 mEq/L
• Band neutrophils: 0 to 100 %
• Chloride: 50 to 175 mEq/L
• Creatinine: 0.1 to 60 mg/dL
• Glucose: 33 to 2000 mg/dL
• Hemoglobin: 0 to 25 g/dL
• Hematocrit: 0 to 75 g/dL
• Platelet count: 0 to 2000 x10^3/mm^3
• Potassium: 0 to 12 mEq/L
• Partial thromboplastin time (PTT): 18.8 to 150 seconds
• Sodium: 50 to 225 mEq/L
• White blood cells (WBC): 0 to 1000 x10^3/mm^3

If our lab measures fall outside these ranges, they will be replaced.

As all the lab measures except bilirubin and PTT fall within the valid range, we take a closer look at bilirubin and PTT.

display(mimic.loc[(mimic['bilirubin'] < 0.1) | (mimic['bilirubin'] > 60), ['bilirubin']])

display(mimic.loc[(mimic['ptt'] < 18.8) | (mimic['ptt'] > 150), ['ptt']])

	bilirubin
6199	0.0
12903	0.0
15526	62.1

	ptt
805	17.50
7952	18.75
8534	18.70

As there are only a few observations that exceed the valid ranges for bilirubin and PTT, and the values aren’t significantly out of range, we choose to leave them as is.

for column in lab_measures:
    plot_histogram_and_boxplot(
        df=mimic,
        column=column)

Albumin, bicarbonate, chloride, and sodium have fairly normal distributions, with extreme values at both the lower and higher ends. The distributions of BUN, bilirubin, lactate, band neutrophils, creatinine, platelet counts, PTT, and WBC are right-skewed, with extreme values at the higher end. Glucose, hematocrit, hemoglobin, and potassium are also right-skewed, but their outliers are present at both the lower and higher ends.

Missing data

We theorize that if a patient is about to be discharged or near the end of their life, their medical information in the past 24 hours will be collected, which will differ for each target class, as we will either see improvements or deterioration. Therefore, we need to examine the medical information based on different target classes.

But first, we look at the missing values.

# dictionary to store missing data information
missing_data_info = {}

# unique classes in target
classes = mimic['death_status'].unique()

for cls in classes:
    # filter based on the class
    class_df = mimic[mimic['death_status'] == cls]
    
    # calculate the percentage of missing values
    missing_data_info[cls] = class_df.isnull().mean() * 100
missing_data_info['overall'] = mimic.isna().mean() * 100
missing_data_df = pd.DataFrame(missing_data_info).iloc[0:-5]

missing_data_df

	0	1	overall
albumin	90.303925	84.083851	89.453001
neutrophils	96.948443	91.692547	96.229421
bicarbonate	3.746770	30.279503	7.376527
bilirubin	84.816045	74.961180	83.467870
bun	3.291497	30.240683	6.978226
chloride	3.556048	29.541925	7.110993
creatinine	3.285345	30.163043	6.962294
dbp	0.326074	1.319876	0.462029
glucose	3.512981	28.843168	6.978226
heart_rate	0.209179	0.271739	0.217738
hematocrit	3.420696	30.357143	7.105682
hemoglobin	4.405070	32.026398	8.183749
lactate	94.899717	72.826087	91.879979
map	0.344531	1.513975	0.504514
ptt	49.864649	50.271739	49.920340
spo2	0.486034	2.445652	0.754116
platelets	4.294328	32.220497	8.114711
potassium	2.713178	28.027950	6.176314
resp_rate	0.486034	0.543478	0.493893
sodium	3.414544	28.998447	6.914498
sbp	0.313769	1.242236	0.440786
temp	0.449120	4.968944	1.067446
wbc	4.275871	32.414596	8.125332

As the columns albumin, band neutrophils, bilirubin, lactate, and PTT have 50% or more missing values regardless of the target class, we have dropped these columns.

mimic = mimic.drop(columns = ['albumin', 'neutrophils', 'bilirubin', 'lactate', 'ptt'])
mimic.head()

	bicarbonate	bun	chloride	creatinine	dbp	glucose	heart_rate	hematocrit	hemoglobin	map	...	resp_rate	sodium	sbp	temp	wbc	age	gender	ethnicity	los	death_status
0	23.0	17.0	96.0	1.3	55.545455	85.0	92.904762	29.6	9.7	75.984845	...	20.363636	131.500000	116.863636	35.930556	10.5	76.0	M	White	6.0646	0
1	14.0	73.0	101.0	5.1	64.047619	118.0	85.750000	35.7	12.2	93.873014	...	14.347826	130.000000	153.523810	36.039682	3.9	66.0	F	White	3.6729	0
2	24.0	33.0	107.0	2.0	76.476190	114.0	81.904762	36.8	12.6	94.850000	...	16.653846	135.666667	141.666667	35.888889	11.1	41.0	M	Other	5.3231	1
3	23.0	29.0	100.0	1.1	75.450000	130.0	94.650000	36.6	12.4	99.066730	...	31.400000	135.000000	146.300000	37.074074	30.2	72.0	M	White	7.6348	1
4	29.0	13.0	104.0	0.4	60.520000	168.5	99.600000	26.9	8.8	78.533332	...	18.840000	138.000000	125.440000	37.687301	14.3	40.0	F	White	3.6660	0

5 rows × 23 columns

Vital signs

We then take a closer look at the target classes in the vital signs and their missing values.

plt.figure(figsize=(10, 6))
    
for column in vital_signs:
    plt.figure(figsize=(10, 6))
    
    for cls in mimic['death_status'].unique():
        subset = mimic[mimic['death_status'] == cls]
        plt.hist(subset[column].dropna(), alpha=0.5, bins=50, label=f'Class {cls}')
    
    plt.title(f'Histogram of {column}')
    plt.xlabel(column)
    plt.ylabel('Frequency')
    plt.legend()
    plt.show()

<Figure size 1000x600 with 0 Axes>

Comparison between the two target groups reveals that patients who did not survive the ICU usually have lower DBP, SBP, MAP, and SpO2 levels. Heart rate, temperature, and respiratory rate do not appear to differ significantly between the classes.

Next, we impute missing values based on the different classes using the RandomSampleImputer from the package feature_engine. This method imputes missing data by drawing random samples from the non-missing values in the same column, preserving the original distribution and maintaining natural variability. Since it uses a range of values from the actual data, it is less likely to introduce systematic bias and maintains the original shape and distribution of the data. The distributions before and after imputation are compared using the Kullback-Leibler Divergence (KLD).

from scipy.stats import entropy

# Function to calculate KLD
def calculate_kld(data, target_col, feature_col, epsilon=1e-10):
    class_0_dist = data[data[target_col] == 0][feature_col].value_counts(normalize=True, sort=False)
    class_1_dist = data[data[target_col] == 1][feature_col].value_counts(normalize=True, sort=False)
    all_values = pd.concat([class_0_dist, class_1_dist], axis=1).fillna(0)
    all_values += epsilon
    all_values.iloc[:, 0] /= all_values.iloc[:, 0].sum()
    all_values.iloc[:, 1] /= all_values.iloc[:, 1].sum()
    kld_value = entropy(all_values.iloc[:, 0], all_values.iloc[:, 1])
    return kld_value

# Calculate KLD before imputation
kld_before_imputation = {col: calculate_kld(mimic, 'death_status', col) for col in vital_signs}

# Impute missing values using median based on classes
data_imputed_median = mimic.copy()
for cls in mimic['death_status'].unique():
    class_data = mimic[mimic['death_status'] == cls]
    for col in vital_signs:
        median_value = class_data[col].median()
        data_imputed_median.loc[mimic['death_status'] == cls, col] = class_data[col].fillna(median_value)

# Calculate KLD after median imputation based on classes
kld_after_median_class_imputation = {col: calculate_kld(data_imputed_median, 'death_status', col) for col in vital_signs}

# Identify columns with missing values within the vital signs
columns_with_missing = [col for col in vital_signs if mimic[col].isnull().any()]

# Impute missing values using RandomSampleImputer based on classes
data_imputed_random_class = mimic.copy()
for cls in mimic['death_status'].unique():
    class_data = mimic[mimic['death_status'] == cls]
    imputer = RandomSampleImputer(variables=columns_with_missing, random_state=0)
    imputer.fit(class_data)
    imputed_class_data = imputer.transform(class_data)
    data_imputed_random_class.loc[mimic['death_status'] == cls] = imputed_class_data

# Calculate KLD after RandomSampleImputer based on classes
kld_after_random_class_imputation = {col: calculate_kld(data_imputed_random_class, 'death_status', col) for col in vital_signs}

# Create a DataFrame to compare KLD values
kld_df = pd.DataFrame({
    'KLD': kld_before_imputation,
    'KLD median imputation': kld_after_median_class_imputation,
    'KLD random sample imputation': kld_after_random_class_imputation
})

# Display the KLD DataFrame
display(kld_df)

	KLD	KLD median imputation	KLD random sample imputation
heart_rate	10.742659	10.753079	10.745013
dbp	10.567222	10.589705	10.571367
sbp	11.638915	11.654600	11.639817
map	12.061363	12.078452	12.059145
temp	10.229210	10.203194	10.238040
spo2	5.321413	5.316279	5.321810
resp_rate	7.820026	7.792015	7.830462

# Plot histograms for each vital sign column before and after imputation
for col in vital_signs:
    plt.figure(figsize=(14, 6))
    
    # Before imputation
    plt.subplot(1, 3, 1)
    for cls in mimic['death_status'].unique():
        subset = mimic[mimic['death_status'] == cls]
        plt.hist(subset[col].dropna(), alpha=0.5, bins=30, label=f'Class {cls}')
    plt.title(f'{col}')
    plt.xlabel(col)
    plt.ylabel('Frequency')
    plt.legend()
    
    # After median class-based imputation
    plt.subplot(1, 3, 2)
    for cls in data_imputed_median['death_status'].unique():
        subset = data_imputed_median[data_imputed_median['death_status'] == cls]
        plt.hist(subset[col].dropna(), alpha=0.5, bins=30, label=f'Class {cls}')
    plt.title(f'{col} median imputation')
    plt.xlabel(col)
    plt.ylabel('Frequency')
    plt.legend()
    
    # After random class-based imputation
    plt.subplot(1, 3, 3)
    for cls in data_imputed_random_class['death_status'].unique():
        subset = data_imputed_random_class[data_imputed_random_class['death_status'] == cls]
        plt.hist(subset[col].dropna(), alpha=0.5, bins=30, label=f'Class {cls}')
    plt.title(f'{col} random sample imputation')
    plt.xlabel(col)
    plt.ylabel('Frequency')
    plt.legend()
    
    plt.tight_layout()
    plt.show()

The KLD values before and after imputation are similar for both the median and random sample imputations. As the random sample imputation is closer to the before-imputation KLD value, we will use the random sample imputation to handle missing values.

# Initialize the RandomSampleImputer for vital signs
imputer = RandomSampleImputer(variables=vital_signs, random_state=0)

# Fit the imputer on the data
imputer.fit(mimic)

# Transform the data
mimic_vital_no_null = imputer.transform(mimic)

# Display the transformed data to verify missing values have been imputed
mimic_vital_no_null[vital_signs].isnull().sum()

heart_rate    0
dbp           0
sbp           0
map           0
temp          0
spo2          0
resp_rate     0
dtype: int64

Lab measures

We next examine the distribution of lab measures for different target classes and their missing values.

plt.figure(figsize=(10, 6))

lab_measures2 = ["bun", "bicarbonate", "chloride", "creatinine", "glucose",
                 "hematocrit", "hemoglobin", "platelets", "potassium", "sodium", "wbc"]

for column in lab_measures2:
    plt.figure(figsize=(10, 6))
    
    for cls in mimic['death_status'].unique():
        subset = mimic[mimic['death_status'] == cls]
        plt.hist(subset[column].dropna(), alpha=0.5, bins=50, label=f'Class {cls}')
    
    plt.title(f'Histogram of {column}')
    plt.xlabel(column)
    plt.ylabel('Frequency')
    plt.legend()
    plt.show()

<Figure size 1000x600 with 0 Axes>

Laboratory measures between patients who survived and those who did not show that BUN, chloride, creatinine, glucose, potassium, sodium, and WBC have similar distributions. However, for patients who did not survive, the measures are lower for bicarbonate, hematocrit, hemoglobin, and platelet counts.

# Calculate KLD before imputation
kld_before_imputation = {col: calculate_kld(mimic, 'death_status', col) for col in lab_measures2}

# Impute missing values using median based on classes
data_imputed_median = mimic.copy()
for cls in mimic['death_status'].unique():
    class_data = mimic[mimic['death_status'] == cls]
    for col in lab_measures2:
        median_value = class_data[col].median()
        data_imputed_median.loc[mimic['death_status'] == cls, col] = class_data[col].fillna(median_value)

# Calculate KLD after median imputation based on classes
kld_after_median_class_imputation = {col: calculate_kld(data_imputed_median, 'death_status', col) for col in lab_measures2}

# Identify columns with missing values within the vital signs
columns_with_missing = [col for col in lab_measures2 if mimic[col].isnull().any()]

# Impute missing values using RandomSampleImputer based on classes
data_imputed_random_class = mimic.copy()
for cls in mimic['death_status'].unique():
    class_data = mimic[mimic['death_status'] == cls]
    imputer = RandomSampleImputer(variables=columns_with_missing, random_state=0)
    imputer.fit(class_data)
    imputed_class_data = imputer.transform(class_data)
    data_imputed_random_class.loc[mimic['death_status'] == cls] = imputed_class_data

# Calculate KLD after RandomSampleImputer based on classes
kld_after_random_class_imputation = {col: calculate_kld(data_imputed_random_class, 'death_status', col) for col in lab_measures2}

# Create a DataFrame to compare KLD values
kld_df = pd.DataFrame({
    'KLD': kld_before_imputation,
    'KLD median imputation': kld_after_median_class_imputation,
    'KLD random sample imputation': kld_after_random_class_imputation
})

# Display the KLD DataFrame
display(kld_df)

	KLD	KLD median imputation	KLD random sample imputation
bun	0.767340	1.095184	0.796221
bicarbonate	0.446083	0.684212	0.446800
chloride	0.320234	0.529884	0.328228
creatinine	0.554858	0.926907	0.552837
glucose	1.161490	1.448877	1.182857
hematocrit	1.766217	2.072636	1.792049
hemoglobin	0.592917	0.882179	0.594489
platelets	2.226841	2.546832	2.255409
potassium	0.547745	0.738254	0.558707
sodium	0.319038	0.648282	0.330599
wbc	1.162038	1.554917	1.206786

# Plot histograms for each vital sign column before and after imputation
for col in lab_measures2:
    plt.figure(figsize=(14, 6))
    
    # Before imputation
    plt.subplot(1, 3, 1)
    for cls in mimic['death_status'].unique():
        subset = mimic[mimic['death_status'] == cls]
        plt.hist(subset[col].dropna(), alpha=0.5, bins=30, label=f'Class {cls}')
    plt.title(f'{col}')
    plt.xlabel(col)
    plt.ylabel('Frequency')
    plt.legend()
    
    # After median class-based imputation
    plt.subplot(1, 3, 2)
    for cls in data_imputed_median['death_status'].unique():
        subset = data_imputed_median[data_imputed_median['death_status'] == cls]
        plt.hist(subset[col].dropna(), alpha=0.5, bins=30, label=f'Class {cls}')
    plt.title(f'{col} median imputation')
    plt.xlabel(col)
    plt.ylabel('Frequency')
    plt.legend()
    
    # After random class-based imputation
    plt.subplot(1, 3, 3)
    for cls in data_imputed_random_class['death_status'].unique():
        subset = data_imputed_random_class[data_imputed_random_class['death_status'] == cls]
        plt.hist(subset[col].dropna(), alpha=0.5, bins=30, label=f'Class {cls}')
    plt.title(f'{col} random sample imputation')
    plt.xlabel(col)
    plt.ylabel('Frequency')
    plt.legend()
    
    plt.tight_layout()
    plt.show()

Similar to the imputation in vital signs, the KLD value of random sample imputation is closer to the original KLD value. The KLD value of median imputation significantly differs from the original KLD value. Furthermore, the distribution of the median imputation shows a noticeable spike in the middle due to the imputed median values. Therefore, we use the random sample imputer to fill missing values.

# Initialize the RandomSampleImputer for vital signs
imputer = RandomSampleImputer(variables=lab_measures2, random_state=0)

# Fit the imputer on the data
imputer.fit(mimic_vital_no_null)

# Transform the data
mimic_no_null = imputer.transform(mimic_vital_no_null)

# Display the transformed data to verify missing values have been imputed
mimic_no_null[lab_measures2].isnull().sum()

bun            0
bicarbonate    0
chloride       0
creatinine     0
glucose        0
hematocrit     0
hemoglobin     0
platelets      0
potassium      0
sodium         0
wbc            0
dtype: int64

mimic_no_null.head()

	bicarbonate	bun	chloride	creatinine	dbp	glucose	heart_rate	hematocrit	hemoglobin	map	...	resp_rate	sodium	sbp	temp	wbc	age	gender	ethnicity	los	death_status
0	23.0	17.0	96.0	1.3	55.545455	85.0	92.904762	29.6	9.7	75.984845	...	20.363636	131.500000	116.863636	35.930556	10.5	76.0	M	White	6.0646	0
1	14.0	73.0	101.0	5.1	64.047619	118.0	85.750000	35.7	12.2	93.873014	...	14.347826	130.000000	153.523810	36.039682	3.9	66.0	F	White	3.6729	0
2	24.0	33.0	107.0	2.0	76.476190	114.0	81.904762	36.8	12.6	94.850000	...	16.653846	135.666667	141.666667	35.888889	11.1	41.0	M	Other	5.3231	1
3	23.0	29.0	100.0	1.1	75.450000	130.0	94.650000	36.6	12.4	99.066730	...	31.400000	135.000000	146.300000	37.074074	30.2	72.0	M	White	7.6348	1
4	29.0	13.0	104.0	0.4	60.520000	168.5	99.600000	26.9	8.8	78.533332	...	18.840000	138.000000	125.440000	37.687301	14.3	40.0	F	White	3.6660	0

5 rows × 23 columns

Outliers

Next, we examine the outliers in the data by first visualizing the numerical data using scatterplots to identify any influential points.

num_features = mimic_no_null.select_dtypes(include=['int64', 'float64']).columns

sns.pairplot(mimic_no_null[num_features], corner=True, diag_kind='kde')

<seaborn.axisgrid.PairGrid at 0x337c3c150>

From the scatterplot, we observe the presence of some influential data points. We also observe a linear correlation between some variables: hemoglobin and hematocrit, sodium and chloride, DBP with SBP and MAP, and SBP and MAP.

As we have multivariate data, using typical outlier analysis tools with z-scores and IQR would be inappropriate as they measure in univariate space. Therefore, we will use the Mahalanobis distance to detect outliers. The Mahalanobis distance is a measure of the distance between a point and a distribution; it is particularly useful for identifying outliers in multivariate space as it accounts for correlations among variables. First, we need to standardize the data.

from sklearn.preprocessing import StandardScaler
from scipy.spatial.distance import mahalanobis
from scipy.stats import chi2

scaler = StandardScaler()

num_features_scaled = scaler.fit_transform(mimic_no_null[num_features])

# Calculate Mahalanobis distance
def calculate_mahalanobis(x, mean, inv_cov_matrix):
    return np.sqrt(mahalanobis(x, mean, inv_cov_matrix))

mean = np.mean(num_features_scaled, axis=0)
cov_matrix = np.cov(num_features_scaled, rowvar=False)
inv_cov_matrix = np.linalg.inv(cov_matrix)

mahalanobis_distances = np.apply_along_axis(calculate_mahalanobis, 1, num_features_scaled, mean, inv_cov_matrix)

# Determine threshold
threshold = chi2.ppf((1 - 0.05), df=num_features_scaled.shape[1])  # 95% confidence interval, df = # of features
outliers = mahalanobis_distances > np.sqrt(threshold) ### threshold is X^2, so sqrt to get threshold of distance

# Remove outliers
mimic_no_outliers = mimic_no_null[~outliers]

print(f"Using the Mahalanobis distance with 95% CI, {mimic_no_null.shape[0]-mimic_no_outliers.shape[0]} outliers were removed.")

Using the Mahalanobis distance with 95% CI, 9 outliers were removed.

Nine data points were outside the 95% Mahalanobis distance and were thus removed. We then explore the collinearity present within the features.

corr_mat = mimic_no_outliers[num_features].corr()
mask = np.triu(np.ones_like(corr_mat, dtype=bool))
np.fill_diagonal(mask, False)

plt.figure(figsize=(30, 20))
sns.heatmap(corr_mat, annot=True, cmap='Blues', mask=mask)
plt.title('Correlation Matrix')

Text(0.5, 1.0, 'Correlation Matrix')

The correlation matrix shows that hemoglobin and hematocrit, as well as MAP with DBP and SBP, are strongly correlated (correlation > 0.80). There are also some variables with high correlation (0.60-0.80): creatinine and BUN, and sodium and chloride. Additionally, SBP and DBP are moderately correlated (0.53).

mimic_no_outliers.to_csv('mimic_clean.csv', header=True)